Seminar

Pansu\'s thesis identifies the kinds of metrics one can get as asymptotic cones of word metrics on nilpotent groups, and Breuillard\'s work both extends this to more kinds of groups and gives very concrete geometric descriptions of the shape of large balls and spheres, with numerous applications. I\'ll describe joint work with Christopher Mooney in which we push forward these explicit descriptions finely enough to understand the dependence on generators in the special case of the 3D Heisenberg group. We give applications to classifying geodesics in CC metrics and in word metrics, and to asymptotic density problems in the discrete and real Heisenberg group.